RNA-binding proteins, particularly splicing factors, localize to sub-nuclear domains termed nuclear speckles. During certain viral infections, as the nucleus fills up with replicating virus compartments, host cell chromatin distribution changes, ending up condensed at the nuclear periphery. In this study we wished to determine the fate of nucleoplasmic RNA-binding proteins and nuclear speckles during the lytic cycle of the Kaposi’s sarcoma associated herpesvirus (KSHV). We found that nuclear speckles became fewer and dramatically larger, localizing at the nuclear periphery, adjacent to the marginalized chromatin. Enlarged nuclear speckles contained splicing factors, whereas other proteins were nucleoplasmically dispersed. Polyadenylated RNA, typically found in nuclear speckles under regular conditions, was also found in foci separated from nuclear speckles in infected cells. Poly(A) foci did not contain lncRNAs known to colocalize with nuclear speckles but contained the poly(A)-binding protein PABPN1. Examination of the localization of spliced viral RNAs revealed that some spliced transcripts could be detected within the nuclear speckles. Since splicing is required for the maturation of certain KSHV transcripts, we suggest that the infected cell does not dismantle nuclear speckles but rearranges their components at the nuclear periphery to possibly serve in splicing and transport of viral RNAs into the cytoplasm.